TE311 Lecture08 DSB SC Modulation

8/10/2019 TE311 Lecture08 DSB SC Modulation

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TE311: Introduction toAnalogue Telecommunications

PART II

Lecture #8Linear Continuous Wave Modulation-II


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IntroductionPoints to be discussed in this lecture

Double Side-band Suppressed Carrier (DSB-SC) Modulation

Generation of DSB-SC Signals

Demodulation of DSB-SC Signals

Quadrature Amplitude Modulation (QAM)


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Double-Sideband Suppressed Carrier(DSB-SC) Modulation

A double-sideband modulated (DSB-SS) signal

( )s t is

defined as follows

( ) ( ) ( )cos 2 cs t m t f t =

( )m t is baseband message signal with bandwidth HzB

cf is the carrier frequency in Hz.


4/23

DSB-SC ModulationFourier transform of a DSB-SC signal is obtainedfrom its time domain description as follows

( ) ( ) ( )1

2 c c

S f M f f M f f = + +

( ) ( )F

m t M f Transmission bandwidth for a DSB-SC signal is

related to the bandwidthT

B

B of the message signal by

2T

B B=


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DSB-SC Modulation

The spectrum of the DSB-SC signal is similar to thatof the AM signal except for the spectral peaks at

cf .

( )m t ( )s t

BB

( )M f

f

cf cf

( )S f

f

cf B+ cf B cf B cf B+

Uppersideband

Lowersideband

( )0M ( )0.5 0M

DSB-SC

modulator


6/23

Generation of DSB-SC SignalsGeneration of a DSB-SC signal is derived from the

time-domain expression i.e. ( ) ( ) ( )cos 2 cs t m t f t = .

( )s t ( )m t

( )cos 2 cf t


7/23

Generation of DSB-SC SignalsBalanced modulator

A DSB-SC signal is generated using two AM signalgenerators in a balanced configuration.

+

AMmodulator

AMmodulator

( )m t

( )2s t

-

( )cos 2 cf t

( )s t ( )m t

( )1s t


8/23


9/23

Generation of DSB-SC SignalsShunt-Bridge Diode Modulator

During the positive half cycles of ( )cos 2 cf t all

diodes are forward biased and ( )0 0v t = .During the negative half cycles of ( )cos 2 cf t all

diodes are reverse biased and ( ) ( )0v t m t = .

( )s t


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Generation of DSB-SC SignalsThus

( ) ( )( ) ( )

( ) ( )

0

0 cos 2 0

cos 2 0

c

c

f tv t

m t f t

m t x t

>=


11/23

Generation of DSB-SC Signals( ) ( ) ( )

( ) ( ) ( ) ( )

0

3

sin / 21 2 cos 22 / 2

c

n

v t m t x t

nm t m t nf t n

=

=

= +

Taking the Fourier transform on both sided gives

( ) ( ) ( ) ( )

( ) ( )23 2

sin1

2

nF

c cnn

Mm t x t M n M n

=

+ + +

where ( ) ( )F

m t M f


12/23

Generation of DSB-SC SignalsPassing through a bandpass fil ter centered at( )0v t c with bandwidth 2Bwhere B is the bandwidth of ( )m t gives

( ) ( ) ( )

2cos 2

c

s t m t f t

=


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Generation of DSB-SC SignalsRing (or Double-Balanced) Modulator

( )s t

During the positive half cycles of ( )cos 2 cf t diodesand are forward biased whereas and are

reverse biased and

1D

3D 2D 4D

( ) ( )0v t m t = .


14/23

Generation of DSB-SC SignalsDuring the negative half cycles of ( )cos 2 cf t diodes

and are reverse biased whereas and are

forward biased and1D 3D 2D 4D

( ) ( )0v t m t = . Thus

( ) ( ) ( )

( ) ( )

( ) ( )

0

cos 2 0

cos 2 0

c

c

m t f t

v t m t f t

m t x t

>=


15/23

Generation of DSB-SC SignalsTaking the Fourier series of ( )x t it follows that

( ) ( ) ( )

( )( ) ( )

0

3

sin / 24 cos 2

/ 2 c

n

v t m t x t

nm t nf t

n

=

=

=

Taking the Fourier transform on both sided gives

( ) ( )

( )

( ) ( )3

sin / 22

/ 2

F

c cn

n

m t x t M n M nn

= + + where ( ) ( )

F

m t M .


16/23

Generation of DSB-SC SignalsPassing through a bandpass fil ter centered at( )0v t c with bandwidth 2B where B is the bandwidth of

( )m t gives

( ) ( ) ( )

4cos 2

c

s t m t f t

=


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Demodulation of DSB-SC SignalsSynchronous Demodulator

Lowpass

filter

( )m t ( )s t ( )s t

( )cos 2

cf t


18/23

Demodulation of DSB-SC SignalsLowpass filter input signal ( )s t

( ) ( ) ( )

( ) ( )

( ) ( ) [ ]

2

cos 2

cos 2

1 1 cos 2 (2 )2 2

c

c

c

s t s t f t

m t f t

m t m t f t

=

=

= +

Lowpass filter output signal

Bandpass signalBaseband signal

( ) ( )1

2

m t m t =


19/23

Quadrature Amplitude Modulation(QAM)

Transmitted signal ( )s t for DSB-SC modulationoccupies twice the bandwidth of the baseband signal

( )m t .

To improve bandwidth utilization efficiency, two DSB-SC signals can be transmitted over the samebandwidth using two phase-quadrature carriers.

Two baseband signals can be separated at thereceiver by synchronous demodulation using twophase-quadrature carriers.


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Such a system is called quadrature amplitude

modulation (QAM) or quadrature multiplexing.

/ 2

( )1m t

( )2m t

( )cos 2 cf t

( )sin 2 cf t

2( )sin(2 )cm t f t

1( )cos(2 )cm t f t

signal

QAM

/ 2

LPF

LPF

( )cos 2 cf t

( )sin 2 cf t

( )2m t

( )1m t

Channel

1( )x t

2( )x t

( )s t


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Transmitted QAM signal ( )s t ( ) ( ) ( ) ( ) ( )1 2cos 2 sin 2c cs t m t f t m t f t = +

Demodulated signals

( ) ( ) ( )( ) ( ) ( ) ( ) ( )

1

1 1 2

2 cos 2

cos 4 sin 4

c

c c

x t s t f t

m t m t f t m t f t

=

= + +

( ) ( ) ( )

( ) ( ) ( ) ( ) ( )

2

2 2 1

2 sin 2

sin 4 sin 4

c

c c

x t s t f t

m t m t f t m t f t

=

= +


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Applying and( )1x t ( )2x t to a lowpass filter withbandwidth equal to the bandwidth of the baseband

signal ( )m t yields ( )and1m t ( ).2m t

Example: Show that a slight error in the phase of thequadrature carriers will result in loss of signals andinterference between channels (co-channel interference).


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Reading Assignments1. B.P. Lathi, Modern Digital and Analog

Communication Systems , Chap. 4, Part 1.

2. Extra reading:

W. Tomasi, Electronic Communications

Systems, Chaps. 4 & 5.

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TE311 Lecture08 DSB SC Modulation